Lightning Review16.2 Electric potential and potential energy due to point chargesSuperposition principle for potentialsPotential energy of a system of point chargesMini-quiz: potential energy of an ion16.3 Potentials and charged conductorsThe electron voltProblem-solving strategyExample : ionization energy of the electron in a hydrogen atom16.4 Equipotential surfaces16.6 The definition of capacitanceUnits of capacitance16.7 The parallel-plate capacitorProblem: parallel-plate capacitor16.8 Combinations of capacitorsa. Parallel combinationParallel combination: notesProblem: parallel combination of capacitorsb. Series combinationSeries combination: notesProblem: series combination of capacitors119/11/20039/11/2003General Physics (PHY 2140)Lecture 5Lecture 5¾ Electrostatics9 Electrical energy9 potential difference and electric potential9 potential energy of charged conductors9 Capacitance and capacitorsChapter 16http://www.physics.wayne.edu/~apetrov/PHY2140/229/11/20039/11/2003Lightning ReviewLightning ReviewLast lecture:1.1.Flux. Gauss’s law.Flux. Gauss’s law.99simplifies computation of electric fieldssimplifies computation of electric fields2.2.Potential and potential energyPotential and potential energy99electrostatic force is conservativeelectrostatic force is conservative99potential (a scalar) can be introduced as potential potential (a scalar) can be introduced as potential energy of electrostatic field per unit chargeenergy of electrostatic field per unit chargeReview Problem:Perhaps you have noticed sudden gushes of rain or hail moments after lightning strokes in thunderstorms. Is there any connection between the gush and the stroke or thunder? Or is this just a coincidence?cosnetoQEAθεΦ= =∑BAPEVV Vq∆∆=−=cloudVCFqE=JJG JGEJGmgJG339/11/20039/11/200316.2 Electric potential and potential energy 16.2 Electric potential and potential energy due to point chargesdue to point chargesElectric circuits: point of zero potential is defined by Electric circuits: point of zero potential is defined by grounding some point in the circuitgrounding some point in the circuitElectric potential due to a point charge at a point in Electric potential due to a point charge at a point in space: point of zero potential is taken at an infinite space: point of zero potential is taken at an infinite distance from the chargedistance from the chargeWith this choice, a potential can be found asWith this choice, a potential can be found asNote: the potential depends only on charge of an object, Note: the potential depends only on charge of an object, qq, and a distance from this object to a point in space, , and a distance from this object to a point in space, rr.eqVkr=.449/11/20039/11/2003Superposition principle for potentialsSuperposition principle for potentialsIf more than one point charge is present, their electric If more than one point charge is present, their electric potential can be found by applying potential can be found by applying superposition superposition principleprincipleThe total electric potential at some point P due to several The total electric potential at some point P due to several point charges is the algebraic sum of the electric point charges is the algebraic sum of the electric potentials due to the individual charges.potentials due to the individual charges.Remember that potentials are scalar quantities!Remember that potentials are scalar quantities!559/11/20039/11/2003Potential energy of a system of point Potential energy of a system of point chargeschargesConsider a system of two particlesConsider a system of two particlesIf VIf V11is the electric potential due to charge qis the electric potential due to charge q11at a point P, at a point P, then work required to bring the charge qthen work required to bring the charge q22from infinity to P from infinity to P without acceleration is qwithout acceleration is q22VV11. If a distance between P and . If a distance between P and qq11is r, then by definitionis r, then by definitionPotential energy is Potential energy is positivepositiveif charges are of the if charges are of the same same signsignand vice versa.and vice versa.PA1221 eqqPE q V kr==q2q1r669/11/20039/11/2003MiniMini--quiz: potential energy of an ionquiz: potential energy of an ionThree ions, Na+, Na+, and Cl-, located such, that they form corners of an equilateraltriangle of side 2 nm in water. What is the electric potential energy of one of the Na+ions?Cl-[]Na Cl Na Na Naee eClNaqq qq qPE k k k q qrrr=+ = +?but : !Cl Naqq=−[]0NaeNaNaqPE k q qr=−+ =Na+Na+779/11/20039/11/200316.3 Potentials and charged conductors16.3 Potentials and charged conductorsRecall that work is opposite of the change in potential Recall that work is opposite of the change in potential energy,energy,No work is required to move a charge between two points No work is required to move a charge between two points that are at the same potential. That is, W=0 if Vthat are at the same potential. That is, W=0 if VBB=V=VA A Recall: Recall: 1.1.all charge of the charged conductor is located on its surfaceall charge of the charged conductor is located on its surface2.2.electric field, E, is always perpendicular to its surface, i.e. electric field, E, is always perpendicular to its surface, i.e. no work is no work is done if charges are moved along the surfacedone if charges are moved along the surfaceThus: potential is constant everywhere on the surface of a Thus: potential is constant everywhere on the surface of a charged conductor in equilibriumcharged conductor in equilibrium[]BAWPEqVV=− =− −… but that’s not all!889/11/20039/11/2003Because the electric field is zero inside the conductor, no Because the electric field is zero inside the conductor, no work is required to move charges between any two work is required to move charges between any two points, i.e. points, i.e. If work is zero, any two points inside the conductor have If work is zero, any two points inside the conductor have the same potential, i.e. potential is constant everywhere the same potential, i.e. potential is constant everywhere inside a conductorinside a conductorFinally, since one of the points can be arbitrarily close to Finally, since one of the points can be arbitrarily close to the surface of the conductor, the surface of the conductor, the electric potential is the electric potential is constant everywhere inside a conductor and equal to its constant everywhere inside a conductor and equal